Simplify the following expression: $ p = \dfrac{n - 10}{-7n + 1} - \dfrac{1}{9} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{n - 10}{-7n + 1} \times \dfrac{9}{9} = \dfrac{9n - 90}{-63n + 9} $ Multiply the second expression by $\dfrac{-7n + 1}{-7n + 1}$ $ \dfrac{1}{9} \times \dfrac{-7n + 1}{-7n + 1} = \dfrac{-7n + 1}{-63n + 9} $ Therefore $ p = \dfrac{9n - 90}{-63n + 9} - \dfrac{-7n + 1}{-63n + 9} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{9n - 90 - (-7n + 1) }{-63n + 9} $ Distribute the negative sign: $p = \dfrac{9n - 90 + 7n - 1}{-63n + 9}$ $p = \dfrac{16n - 91}{-63n + 9}$ Simplify the expression by dividing the numerator and denominator by -1: $p = \dfrac{-16n + 91}{63n - 9}$